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 August 27th, 2016, 03:03 PM #1 Newbie   Joined: Aug 2016 From: Brazil Posts: 8 Thanks: 0 calculate angle x In the figure, AB=AC and HN=MN. Calculate measure of angle x.123.jpg Thank you. Answer x=90° Last edited by skipjack; October 28th, 2018 at 09:00 PM.
 August 28th, 2016, 05:16 PM #2 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,417 Thanks: 1025 You posted 8 problems, but showed no attempts at solutions. Are you trying to get your homework done here? Concerning this problem, since posted in "Geometry section", is it assumed that no trigonometry is allowed?
August 28th, 2016, 06:20 PM   #3
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 Originally Posted by Nathalia In the figure, AB=AC and HN=MN. Calculate measure of angle x.Attachment 7905 Thank you. Answer x=90°
In general, this is not true. Move point $\displaystyle M$ closer to point $\displaystyle C$ and the angle $\displaystyle X$ becomes obtuse.

Last edited by skipjack; October 28th, 2018 at 09:01 PM.

August 28th, 2016, 07:25 PM   #4
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 Originally Posted by mrtwhs In general, this is not true. Move point $\displaystyle M$ closer to point $\displaystyle C$ and the angle $\displaystyle X$ becomes obtuse.
You mean "only works when point M is at center of BC", right?

Last edited by skipjack; October 28th, 2018 at 09:01 PM.

August 29th, 2016, 06:54 AM   #5
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 Originally Posted by Denis You mean "only works when point M is at center of BC", right?
Yes, that is what I meant. Even though I was born and educated in the U.S., in school I took English as a foreign language.

Last edited by skipjack; October 28th, 2018 at 09:02 PM.

August 29th, 2016, 08:06 AM   #6
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 Originally Posted by mrtwhs ...in school I took English as a foreign language.
So did I: mother tongue = French.
Dad Irish, Mom French...and the BOSS!!

 October 28th, 2018, 02:09 PM #7 Newbie   Joined: Oct 2018 From: usa Posts: 1 Thanks: 0 Let I be the point of intersection of (AN) and (HC) angle AMN = angle (HBC) ...... (1) BM/AM = BH/HM THEN 2(BM/AM) = BH/(HM/2) OR BC/AM = BH/MN SO BC/BH = AM/MN ........ (2) (1) AND (2) MEANS THAT THE 2 TRIANGLES CBH AND AMN ARE SIMILAR AND ANGLE NAM = ANGLE HCB THEREFORE THE QUADRILATERAL AIMC IS CYCLIC AND x = 90° Last edited by skipjack; October 28th, 2018 at 11:15 PM.

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